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 A287688 Triangle read by rows: T(j,k) is the number of distinct edge segment pairs in a j X k rectangular grid. 2
 2, 6, 7, 10, 15, 13, 15, 21, 28, 22, 21, 28, 36, 45, 32, 28, 36, 45, 55, 66, 45, 36, 45, 55, 66, 78, 91, 59, 45, 55, 66, 78, 91, 105, 120, 76, 55, 66, 78, 91, 105, 120, 136, 153, 94, 66, 78, 91, 105, 120, 136, 153, 171, 190, 115, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 137 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This gives the number of pairs of edge segments that are distinct with respect to rotation and mirror images. Sequence is arranged so that j <= k (since 2 X 3 and 3 X 2 are equivalent grids), first by increasing j, then by increasing k: a(1) = 1 X 1 = 2, a(2) = 1 X 2 = 6, a(3) = 2 X 2 = 7, a(4) = 1 X 3 = 10. Here j = A002260(n), k = A002024(n), and n = A000217(k-1) + j. Where j != k, a(n) = A000217(j + k). Where j = k, a(n) is approximately A236312(j-2); a(n) >= A236312(j-2). LINKS Doug Bell, Table of n, a(n) for n = 1..11325, rows n = 1..150, flattened. EXAMPLE Triangle begins:    2;    6,  7;   10, 15, 13;   15, 21, 28, 22;   21, 28, 36, 45, 32;   28, 36, 45, 55, 66, 45;   36, 45, 55, 66, 78, 91, 59; ... For n = 3, the a(3) = 7 pairs of edge segments for a 2 X 2 rectangular grid are:   + - - +     + * * +  + * - +  + * - +  + * - +  + * - +  + * - +  + * - +   |     | --\ |     |  |     *  |     |  |     |  |     |  |     |  *     |   |     | --/ |     |  |     |  |     *  |     |  |     |  *     |  |     |   + - - +     + - - +, + - - +, + - - +, + - * +, + * - +, + - - +, + - - +. CROSSREFS Cf. A002260, A002024, A000217, A236312. Distinct edge segments A287618. Sequence in context: A047552 A287453 A287449 * A221847 A283766 A047216 Adjacent sequences:  A287685 A287686 A287687 * A287689 A287690 A287691 KEYWORD nonn,tabl AUTHOR Doug Bell, May 29 2017 STATUS approved

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Last modified February 22 10:19 EST 2020. Contains 332134 sequences. (Running on oeis4.)